In so-called half engine operation, half of the cylinders of the internal combustion engine do not participate in the combustion process by having their intake and exhaust valves as well as their fuel injection switched off, which compared to full engine operation, in which the intake and exhaust valves as well as the fuel injection of all cylinders are activated, allows for fuel savings. The intake and exhaust valves are generally also referred to as gas-exchange valves. The times at which the gas-exchange valves may be deactivated or activated are limited by the base circle of the camshaft operating the respective gas-exchange valve, since the corresponding gas-exchange valve is in the powerless rest state only on the base circle of the camshaft. Half engine operation is possible only in a limited operating range of the internal combustion engine. FIG. 2 shows the operating range of half engine operation shaded in a diagram of the engine torque Md plotted against the engine speed nmot. Half engine operation is accordingly possible only in an operating range in which for engine speed nmot: nmot1≦nmot≦nmot2. Furthermore, half engine operation is possible only in an operating range of the internal combustion engine, in which for engine torque Md of the internal combustion engine: 0 ≦Md ≦Md1. In this instance, nmot1 represents a first engine speed threshold, nmot2 a second engine speed threshold and Md1 an engine torque threshold. Within the operating range limited by the mentioned threshold values as represented in a shaded manner in FIG. 2, the internal combustion engine may be operated in half engine operation, outside of this operating range in full engine operation. In a transition of the operating state of the internal combustion engine from the operating range of full engine operation into the operating range of half engine operation shown in a shaded manner in FIG. 2, a switchover request is produced, in response to which the intake and exhaust valves of half of the cylinders are switched off and the fuel supply associated with these cylinders is deactivated. If conversely a transition is made from the operating range of half engine operation into the operating range of full engine operation, then a switchover request is produced, in response to which all of the switched-off intake and exhaust valves are switched on again and the fuel supply associated with the corresponding cylinders is activated again.